In one corner, we have a financially fortunate homebuyer with a $400,000 mortgage. In the other corner, we have a more financially modest buyer with a $100,000 mortgage. Who will win the battle for the best mortgage deal?

Not the frugal buyer, says Zillow Mortgages.

Mortgage loan borrowers with low loan amounts of about $100,000 tend to pay 10 percent more than borrowers with high loan amounts of around $400,000, according to a recent Zillow Mortgages analysis of loan requests and quotes. More than a quarter of all U.S. homes would have a mortgage of $100,000 or less if 20 percent were put down on the home, said Zillow.

The analysis found more bad news for borrowers with low loan amounts: They also have limited loan options. According to Zillow Mortgages, a typical borrower seeking a $100,000 loan received half as many loan quotes from lenders compared to similar borrowers seeking loans for $400,000.

“Lenders go after big loan amounts and back-burner small loan amounts because even though they take the same amount of time to complete, the larger the loan amount is, the more a lender typically makes,” said Erin Lantz, vice president of mortgages at Zillow. “Since there is less competition for small loan amounts, lenders offer higher interest rates to help cover the costs, and many low- to middle-income borrowers have no choice but to pay more.”

These borrowers are actually being offered more expensive loans compared to borrowers with high loan amounts. Zillow Mortgages broke down that comparison in stark terms: The borrower with the $100,000 loan is currently being offered an average interest rate of 3.95 percent, with an APR of 4.06 percent. The borrower with the $400,000 loan is being offered a 3.64-percent interest rate, with an APR of 3.7 percent.

Those may seem like modest differences, but when calculating the difference in what each buyer will pay in interest over the life of his loan, it adds up — and the larger the difference between the interest rate and the APR, the more it costs the homebuyer per dollar borrowed. If a borrower with a $100,000 loan were offered the same interest rate and APR as a borrower with a $400,000 loan, they would save 4 percent per month — or $7,560 — over the life of a 30-year fixed-rate loan, Zillow Mortgages noted.

The news gets more sobering on even lower loan amounts. If a homebuyer snags a property for about $50,000, he may be offered an average interest rate of 3.9 percent, with an APR of 4.14 percent, and have 88 percent fewer loan quotes from one-sixth as many lender as similar borrowers seeking loans for $400,000. Loans for $50,000 cost an average of 12 percent more than loans for $400,000, Zillow Mortgages said.